because the center of one end is not in line with the

center of the other end. The three parts consist of an

upper and a lower section that are truncated rectangular

prisms. The third section is a truncated oblique

pyramid.

1. Draw the orthographic views, extending the

lines of the sides of the pyramid to its apex in

both views (view A).

2. Rotate the lines of the sides to the horizontal in

the top view. Project the points located on the

front view and draw the true-length lines (view

W

3. At one side of the views, develop the surface of

the oblique square pyramid. Construct one

triangle at a time, and take the length of the three

sides of each triangle from the views (view C).

Draw the upper edges to complete the drawing.

4. Draw the surface patterns of the upper and lower

prisms (view D).

The development of a cone is similar to the

development of a pyramid. Consider it a pyramid with

2. Develop the surface pattern of the cone using

an infinite number of sides. In actual practice, of

the length from the apex to the base as a radius

course, the number of sides are drawn on the

for drawing the arc. Step off on this line the

orthographic views and projected to the development.

equally spaced division of the base. Then,

The steps in developing a truncated right cone are

measure each element individually and transfer

shown in figure 14-53.

this measurement to the development. The ends

The truncated right cone has a center line that is

of each of these elements define the curve of the

perpendicular to its base. The elements on a right cone

upper edge of the peripheral surface (view B).

are all the same length. The true length of these

3. Draw the base surface circle and the top surface

elements is shown by those that fall to the extreme right

ellipse attached to the peripheral surface (view

and left in a front view. These elements are horizontal

lines in a top view. A slanting plane cuts the cone in

C).

figure 14-53. The end points of the elements between

the two outside elements must project to one of the

outside lines to determine their true lengths.

To develop a truncated right cone, use the following

Triangulation is slower and more difficult than

steps:

parallel line or radial development, but it is more

practical for many types of figures. It is the only

1. Draw the orthographic views. Include either a

method with which the development of warped surfaces

side view (view A) or an auxiliary view of the

may be approximated. In development of triangulation,

ellipse formed by the slanting plane. Note that

the piece is divided into a series of triangles, as in radial

the center of the ellipse must be determined

development. However, there is no one single apex for

since it does not fall on the center line of the

the triangles. The problem becomes one of finding the

cone. This center point is projected to the side

true lengths of the varying oblique lines. This is usually

view and defines the length of the minor axis of

done by drawing a true-length diagram.

the ellipse. The length of the major axis is

defined by the length of the slanting line in the

front view.

14-33